Math calculus
posted by Jake
a cylindrical vat must hold 5m^3, the vat must be wider than it is tall, but no more than 3 m in diameter. What dimensions will use the least amount of material?

Steve
v = πr^2h = 5, so
h = 5/(πr^2)
a = 2πr^2 + 2πrh
= 2πr^2 + 10/r
da/dr = 4πr  10/r^2
da/dr=0 when 4πr^3=10
r = ∛(5/(2π))
h = 5/(πr^2) = 5/(π(5/(2π))^(2/3)) = ∛(20/π)
since 3 > 2r > h, it works.
Respond to this Question
Similar Questions

Calculus
1. Chris makes an opentopped box from a 30cm by 30cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square to the nearest hundredth of … 
Math 209
Draining the vat. With only the small valve open, all of the liquid can be drained from a large vat in 4 hours. With only the large valve open, all of the liquid can be drained from the same vat in 2 hours. How long would it take to … 
Physics
A vat in England nicknamed "Strongbow" is 19.7 m tall, but how wide is it? 
Physics
A vat in England nicknamed "Strongbow" is 19.7 m tall, but how wide is it? 
Calculus
A metal cylindrical container with an open top is to hold 1 cubic foot. If there is no waste in construction, find the dimensions which will require the least amount of material. 
Maths lit
Good people can you please help me on how to calculate exclusive Vat and inclusive Vat and price before Vat. Any answer accepted 
maths
A contractor supplied some items to a school. The contractor's bill is shown below. If each amount includes 5% VAT calculate how much the government receives as VAT. Electrical fittings = #52 500. 
MATHS plzz help ASAP
while paying a bill a man paid $189.80 as the amount of VAT at 13%. how much was the actual bill amount? 
maths
An exercise machine is marked at $2400 before VAT at 15% is included. a) calculate the VAT b) calculate the cost after VAT c) If 20% discount was given to the customer before the VAT was included. What discount but before the VAT? 
math
Item cost $6750 vat inclusive. If VAT was charged at 12.5% what was the cost of the item before VAT?